Abstract. We will give an overview of the Strichartz and Space Time Integral estimates for
the Klein-Gordon and subcritical nonlinear Klein-Gordon equations, respectively. In this frame-
work, the regularity of the solution and scattering operators for the nonlinear subcritical Klein-
Gordon is studied, mainly using these tools and estimates of the nonlinearity in Besov spaces.
We prove that these operators are (uniformly) Hölder continuous on the energy space for space
dimension n >= 3, and Lipschitz continuous for n <= 8.
AMS Subject Classification: 35L71, 35L10, 46E35.

Länka till denna publikation

Dela på webben

Skapa referens, olika format (klipp och klistra)

BibTeX @article{Brenner2011,author={Brenner, Philip},title={Lipschitz continuity of the scattering operator for nonlinear Klein-Gordon equations},journal={Applied and Computational Mathematics},issn={1683-3511},volume={10},issue={2},pages={213-241},abstract={Abstract. We will give an overview of the Strichartz and Space Time Integral estimates for
the Klein-Gordon and subcritical nonlinear Klein-Gordon equations, respectively. In this frame-
work, the regularity of the solution and scattering operators for the nonlinear subcritical Klein-
Gordon is studied, mainly using these tools and estimates of the nonlinearity in Besov spaces.
We prove that these operators are (uniformly) Hölder continuous on the energy space for space
dimension n >= 3, and Lipschitz continuous for n <= 8.
AMS Subject Classification: 35L71, 35L10, 46E35.},year={2011},keywords={Nonlinear Klein-Gordon Equations, Space Time Integral Estimates, Strichartz In- equalities, Regularity of Solution- and Scattering Operators, Lipschitz Continuity},}

RefWorks RT Journal ArticleSR ElectronicID 144224A1 Brenner, PhilipT1 Lipschitz continuity of the scattering operator for nonlinear Klein-Gordon equationsYR 2011JF Applied and Computational MathematicsSN 1683-3511VO 10IS 2SP 213OP 241AB Abstract. We will give an overview of the Strichartz and Space Time Integral estimates for
the Klein-Gordon and subcritical nonlinear Klein-Gordon equations, respectively. In this frame-
work, the regularity of the solution and scattering operators for the nonlinear subcritical Klein-
Gordon is studied, mainly using these tools and estimates of the nonlinearity in Besov spaces.
We prove that these operators are (uniformly) Hölder continuous on the energy space for space
dimension n >= 3, and Lipschitz continuous for n <= 8.
AMS Subject Classification: 35L71, 35L10, 46E35.LA engLK http://www.acmij.az/view.php?lang=az&menu=journal&id=48OL 30